Answer :
Let's solve the equation [tex]\(4|x+5|=28\)[/tex].
1. Isolate the absolute value expression:
Divide both sides of the equation by 4 to simplify:
[tex]\[
|x+5| = \frac{28}{4} = 7
\][/tex]
2. Solve the equation without absolute value:
The equation [tex]\(|x+5| = 7\)[/tex] means that the expression inside the absolute value can be either 7 or -7. So, we set up two separate equations to solve for [tex]\(x\)[/tex]:
- Equation 1: [tex]\(x + 5 = 7\)[/tex]
Subtract 5 from both sides:
[tex]\[
x = 7 - 5 = 2
\][/tex]
- Equation 2: [tex]\(x + 5 = -7\)[/tex]
Subtract 5 from both sides:
[tex]\[
x = -7 - 5 = -12
\][/tex]
3. Conclusion:
The solutions to the equation [tex]\(4|x+5|=28\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = -12\)[/tex].
Therefore, the correct answer is:
D. [tex]\(x = -12\)[/tex] and [tex]\(x = 2\)[/tex]
1. Isolate the absolute value expression:
Divide both sides of the equation by 4 to simplify:
[tex]\[
|x+5| = \frac{28}{4} = 7
\][/tex]
2. Solve the equation without absolute value:
The equation [tex]\(|x+5| = 7\)[/tex] means that the expression inside the absolute value can be either 7 or -7. So, we set up two separate equations to solve for [tex]\(x\)[/tex]:
- Equation 1: [tex]\(x + 5 = 7\)[/tex]
Subtract 5 from both sides:
[tex]\[
x = 7 - 5 = 2
\][/tex]
- Equation 2: [tex]\(x + 5 = -7\)[/tex]
Subtract 5 from both sides:
[tex]\[
x = -7 - 5 = -12
\][/tex]
3. Conclusion:
The solutions to the equation [tex]\(4|x+5|=28\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = -12\)[/tex].
Therefore, the correct answer is:
D. [tex]\(x = -12\)[/tex] and [tex]\(x = 2\)[/tex]